85 



a simple special case to draw up a formula here, which is in 

 agreement with what is known concerning- the kinetic energy. This 

 special case is the following. 



A large number n^ of particles move in a space V, which has 

 the following properties : the pai-ticles can move freely in a part of 

 the space without being subjected to forces, I will call this part the 

 free space. In another part v forces will act which are directed 

 towards a centre; the intensity of these forces will be proportional 

 to the distance from that centre. We will assume that not only one 

 centre of this kind is present in the space, but n^, each of them 

 surrounded by a region v. Every region v, however, will be 

 surrounded by a transition region, which is characterised by the 

 property that a particle lying in it has a much higher potential 

 energy than one in the free space. In other words: when the 

 particles come from the free space and j^enetrate into the transition- 

 regions the}' are at first repulsed, and not until they have approached 

 towards the centre to within a definite distance 7^ will they experience 

 the forces directed towards the centre, which I will call the quasi- 

 elastic forces. I will assume, that the sum of all the regions v and 

 also of the transition-regions will be small compared with the free 

 space. This latter may therefore also be represented approximately 

 by F. 



It is obvious that in each of the regions v particles can move 

 which execute harmonic vibrations. The period of these vibrations 

 will be determined by the mass of the particles and by the intensity 

 of the quasi-elastic forces. We will raise the question, what will be 

 the distribution in velocity and the distribution in configuration of 

 these particles. 



I will asscme that the component of the velocity in the direction 

 of the radius-vector towards the centre of attraction will show a 

 smaller amount than would agree with the equipartition law; but 

 that the components perpendicular to it will show the normal equi- 

 partition amount. I make this assumption in order to account for the 

 energy of di-atomic molecules, which corresponds at ordinary tem- 

 peratures with five degrees of freedom. In reality, however, the 

 properties of di-atomic molecules will probably be somewhat different 

 from those assumed by me. The average kinetic energy of the com- 

 ponent of the velocity in the direction of the radius vector of par- 

 ticles which lie in the regions v will be represented instead of by 



vh 

 the normal \ S, by the value ascribed to it by Planck : 



vh 



— 1 



